2025/11/24 by Qiu, Chenyang, Qian, Yangyang, Lin, Zongli +1
Computer Science · #Affine transformation #Convex function #Convex optimization #Distributed Control Multi-Agent Systems #Distributed Sensor Networks and Detection Algorithms #Duality (order theory) #FOS: Electrical engineering #FOS: Mathematics #Linear matrix inequality #Linearization #Neural Networks Stability and Synchronization #Optimization and Control (math.OC) #Optimization problem #Quadratic equation #Separable space #Subgradient method #Systems and Control (eess.SY) #electronic engineering #information engineering
paper · open access · doi:10.48550/arxiv.2511.19708
published in arXiv (Cornell University) (Cornell University)
openalex publication_date 2025/11/24 · openalex created_date 2025/11/28 · openalex updated_date 2026/07/28
This paper studies distributed convex optimization with both affine equality and nonlinear inequality couplings through the duality analysis. We first formulate the dual of the coupling-constraint problem and reformulate it as a consensus optimization problem over a connected network. To efficiently solve this dual problem and hence the primal problem, we design an accelerated linearized algorithm that, at each round, a look-ahead linearization of the separable objective is combined with a quadratic penalty on the Laplacian constraint, a proximal step, and an aggregation of iterations. On the theory side, we prove non-ergodic rates for both the primal optimality error and the feasibility error. On the other hand, numerical experiments show a faster decrease of optimality error and feasibility residual than augmented-Lagrangian tracking and distributed subgradient baselines under the same communication budget.